import numpy as np

X = 2 * np.random.rand(100,1)
y = 4 + 3 * X + np.random.randn(100,1)

X_b = np.c_[np.ones((100,1)), X]    # add x0 = 1 to each instance
theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)
print(theta_best)

X_new = np.array([[0], [2]])
X_new_b = np.c_[np.ones((2,1)), X_new]  # add x0 = 1 to each instance
y_predict = X_new_b.dot(theta_best)
print(y_predict)


